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An approximation property of certain nonlinear Volterra integral operators

Part of: Volterra integral equations Approximations and expansions

Published online by Cambridge University Press:  26 February 2010

Hermann Brunner
Hermann Brunner
Affiliation:
Department of Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada.
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Extract

Let T be a nonlinear Volterra integral operator of the form

(with I compact, a < b), whose kernel K = K(x, t, u) satisfies the following conditions:

with

MSC classification

Secondary: 41A50: Best approximation, Chebyshev systems 45D05: Volterra integral equations
Type
Research Article
Information
Mathematika , Volume 23 , Issue 1 , June 1976 , pp. 45 - 50
Copyright
Copyright © University College London 1976

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References

1.Barrar, R. B. and Loeb, H. L.. “On the continuity of the nonlinear Tschebyscheff operator”, Pacific J. Math., 32 (1970), 593–601.CrossRefGoogle Scholar
2.Brunner, H.. “On the approximate solution of first-kind integral equations of Volterra type”, Computing (Arch. Elektron. Rechneri), 13 (1974), 67–79.Google Scholar
3.Collatz, L. and Krabs, W.. “Approximationstheorie (B. G. Teubner, Stuttgart, 1973).CrossRefGoogle Scholar
4.Dunham, C. B.. “Existence and continuity of the Chebyshev operator”, SIAM Review, 10 (1968), 444–446.CrossRefGoogle Scholar
5.Dunham, C. B.. “Chebyshev approximation with a null point”, Z. Angew. Math. Mech., 52 (1972), 239.CrossRefGoogle Scholar
6.Dunham, C. B.. “Families satisfying the Haar condition”, J. Approx. Theory, 12 (1974), 291–298.CrossRefGoogle Scholar
7.Gantmacher, F. R. and Krein, M. G.. Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme (Akademie-Verlag, Berlin, 1960).Google Scholar
8.Janikowski, J.. “Equation integrate non lineaire d'Abel”, Bull. Soc. Sci. Lettres Lódz, 13 (1962), No. 11.Google Scholar
9.Kaufman, E. H. and Belford, G. G.. “Transformation of families of approximating functions”, J. Approx. Theory, 4 (1971), 363–371.CrossRefGoogle Scholar